
from IPython.core.interactiveshell import InteractiveShell
InteractiveShell.ast_node_interactivity = "all"


import math
import scipy
import nlopt
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import datetime as dt

import statsmodels.api as sma
from statsmodels.regression.quantile_regression import QuantReg as qr
from datetime import datetime


path = "D:\\Data\\"


start = dt.datetime(year=2002, month=12, day=31)
end = dt.datetime(year=2021, month=12, day=31)


#! pip install nlopt
#! pip install yfinance
#! pip install pandas_datareader


#path = "/home/jovyan/demo/Data/"


window_size = 52 * 3


def historical_var(stock_name, q, window_size = window_size, stocks_losses_series = stocks_losses_W_pct):
    return stocks_losses_series[stock_name].dropna().rolling(
        window = window_size, min_periods = int(0.8 * window_size)
    ).apply(lambda x: np.quantile(x, q)).dropna().rename(stock_name + "_VaR_" + str(q))


def formula_var(stock_name, q, window_size = window_size, stocks_losses_series = stocks_losses_W_pct):
    rolling = stocks_losses_series[stock_name].dropna().rolling(window = window_size, min_periods = int(0.8 * window_size))
    mean_series = rolling.mean()
    std_series = rolling.std()
    return (mean_series + scipy.stats.norm.ppf(q) * std_series).dropna().rename(stock_name + "_VaR_" + str(q))


def Trs(df):
    return np.array(df.T)[0]

def regularize(series_i, market_losses_series, state_variables_series):
    series_i = series_i.dropna().copy()
    mkt = market_losses_series.copy()
    svs_lagged = state_variables_series.copy().shift(1).dropna()
    common = svs_lagged.index.intersection(series_i.index)
    mkt = mkt.loc[common,:]
    series_i = series_i.loc[common]
    svs_lagged = svs_lagged.loc[common,:]
    return series_i, mkt, svs_lagged


def log_likelihood_norm(params, series_i, mkt, svs_lagged):
    pi = math.pi
    n = series_i.shape[0]
    mu, sigma, p0, p1_0, p1_1, p1_2, p1_3, p1_4, p1_5, p1_6, p2, p3, p4_0, p4_1, p4_2, p4_3, p4_4, p4_5, p4_6, p5 = params
    p1_v = np.array([p1_0, p1_1, p1_2, p1_3, p1_4, p1_5, p1_6])
    p4_v = np.array([p4_0, p4_1, p4_2, p4_3, p4_4, p4_5, p4_6])

    part1 = (-n) * np.log(sigma)
    part2 = (-n / 2) * np.log(2 * pi)
    part3 = (-1.0 / 2 / np.power(sigma, 2)) * (sum(np.power(
            mu - (Trs(mkt) - p0 - p1_v.dot(svs_lagged.T) - p2 * Trs(series_i))
                / (p3 + p4_v.dot(svs_lagged.T) + p5 * Trs(series_i)), 2)))
    ll = part1 + part2 + part3
    return ll


def fit_mle_norm(series_i, mkt, svs_lagged, initial_guess = None):

    def mle_objective(temp, grad):
        assert len(grad) == 0
        assert len(temp) == 20
        return -log_likelihood_norm(temp, series_i, mkt, svs_lagged)

    lb = [-10, 0] + [-10] + [-1, -5, -0.3, -6, -4, -3, -10] + [-5, -10] + [-1, -5, -0.3, -6, -4, -3, -10] + [-5]
    ub = [10, 10] + [10] + [1, 5, 0.3, 6, 4, 3, 10] + [5, 10] + [1, 5, 0.3, 6, 4, 3, 10] + [5]
    opt = nlopt.opt(nlopt.LN_COBYLA, 20)
    opt.set_lower_bounds(lb)
    opt.set_upper_bounds(ub)
    opt.set_min_objective(mle_objective)
    opt.set_xtol_rel(1e-2)
    opt.set_ftol_abs(1e-3)

    if initial_guess is None:
        x0 = [0.2] * 20
    else:
        x0 = initial_guess
    x = opt.optimize(x0)

    assert opt.last_optimize_result() in [nlopt.SUCCESS, nlopt.FTOL_REACHED, nlopt.XTOL_REACHED]
    # print(x)
    return x


def MLE_var_result(params, stock_name, q, series_i, mkt, svs_lagged):
    mu, sigma, p0, p1_0, p1_1, p1_2, p1_3, p1_4, p1_5, p1_6, p2, p3, p4_0, p4_1, p4_2, p4_3, p4_4, p4_5, p4_6, p5 = params
    p1_v = np.array([p1_0, p1_1, p1_2, p1_3, p1_4, p1_5, p1_6])
    p4_v = np.array([p4_0, p4_1, p4_2, p4_3, p4_4, p4_5, p4_6])

    loc_series = p0 + p1_v.dot(svs_lagged.T) + p2 * Trs(series_i)
    scale_series = p3 + p4_v.dot(svs_lagged.T) + p5 * Trs(series_i)
    err_series = (Trs(mkt) - loc_series) / scale_series
    var_series = []
    for i in range(err_series.shape[0]):
        var_series.append(scipy.stats.norm(loc_series[i] + mu * scale_series[i], scale_series[i] * sigma).ppf(q))
    loc_series = pd.Series(loc_series, index = mkt.index, name = "loc")
    scale_series = pd.Series(scale_series, index = mkt.index, name = "scale")
    var_series = pd.Series(var_series, index = mkt.index, name = stock_name + "_VaR_" + str(q))
    error_series = pd.Series(err_series, index = mkt.index, name = "error_term")
    return var_series, (mu, sigma), pd.concat([var_series, error_series, loc_series, scale_series], axis = 1)


def MLE_var(stock_name, q,
            market_losses_series = market_losses_W_pct,
            stocks_losses_series = stocks_losses_W_pct,
            state_variables_series = stateVariables_W):

    stk, mkt, svs_lagged = regularize(stocks_losses_series[stock_name], market_losses_series, state_variables_series)
    params = fit_mle_norm(stk, mkt, svs_lagged)
    return MLE_var_result(params, stock_name, q, stk, mkt, svs_lagged)


def qr_var(stock_name, q, modified = True,
           state_variables_series = stateVariables_W,
           stocks_losses_series = stocks_losses_W_pct):

    stk = stocks_losses_series[stock_name].dropna().copy()
    svs_lagged = state_variables_series.copy().shift(1).dropna()
    if modified:
        stk_lagged = stk.shift(1).dropna()
        common = stk_lagged.index.intersection(svs_lagged.index)
        stk = stk.loc[common]
        reg = svs_lagged.loc[common,:]
        reg["stock_lagged"] = stk_lagged.loc[common]
    else:
        common = stk.index.intersection(svs_lagged.index)
        stk = stk.loc[common]
        reg = svs_lagged.loc[common,:]

    qr_model = qr(stk, sma.add_constant(reg)).fit(q)
    qr_var_values = qr_model.fittedvalues.rename(stock_name + "_VaR_" + str(q))
    return qr_var_values, qr_model


def var(stock_name, q, qr_var_method, qr_var_modified = True):
    if qr_var_method != qr_var and qr_var_modified == False:
        raise Exception("Input Error! Only Quantile Regression VaR model can be modified!")
    if qr_var_method == qr_var:
        if qr_var_modified:
            stk_var = qr_var_method(stock_name, q)[0]
        else:
            stk_var = qr_var_method(stock_name, q, modified = False)[0]
    elif qr_var_method == MLE_var:
        stk_var = qr_var_method(stock_name, q)[0]
    else:
        stk_var = qr_var_method(stock_name, q)
    return stk_var


def qr_covar(stock_name, q, qr_var_method, qr_var_modified = True,
             state_variables_series = stateVariables_W,
             market_losses_series = market_losses_W_pct):

    stk_var = var(stock_name, q, qr_var_method, qr_var_modified)
    mkt = market_losses_series.copy()
    svs_lagged = state_variables_series.copy().shift(1).dropna()

    common = svs_lagged.index.intersection(stk_var.index)
    mkt = mkt.loc[common,:]
    reg = svs_lagged.loc[common,:]
    reg[stk_var.name] = stk_var.loc[common]

    qr_model = qr(mkt, sma.add_constant(reg)).fit(q)
    qr_covar_values = qr_model.fittedvalues.rename(stock_name + "_CoVaR_" + str(q))

    return qr_covar_values, qr_model, stk_var


def qr_delta_covar(stock_name, q, qr_var_method, qr_var_modified = True,
                   formula_alter = True):

    if q <= 0.5 and q >= 1:
        raise Exception("Input Error! q should be in (0.5, 1)!")

    if formula_alter:
        _, qr_model_q, stk_var = qr_covar(stock_name, q, qr_var)
        var_median = qr_covar(stock_name, 0.5, qr_var)[2]
        return ((stk_var - var_median) * qr_model_q.params[-1]).rename(stock_name + "_\u0394CoVaR_" + str(q) + "_formula2"), stk_var
    else:
        covar_qr, _, stk_var = qr_covar(stock_name, q, qr_var)
        temp = covar_qr - qr_covar(stock_name, 0.5, qr_var)[0]
        return temp.rename(stock_name + "_\u0394CoVaR_" + str(q) + "_formula1"), stk_var


def MLE_covar_result(params, stock_name, q, series_i, mkt, svs_lagged):
    mu, sigma, p0, p1_0, p1_1, p1_2, p1_3, p1_4, p1_5, p1_6, p2, p3, p4_0, p4_1, p4_2, p4_3, p4_4, p4_5, p4_6, p5 = params
    p1_v = np.array([p1_0, p1_1, p1_2, p1_3, p1_4, p1_5, p1_6])
    p4_v = np.array([p4_0, p4_1, p4_2, p4_3, p4_4, p4_5, p4_6])

    loc_series = p0 + p1_v.dot(svs_lagged.T) + p2 * Trs(series_i)
    scale_series = p3 + p4_v.dot(svs_lagged.T) + p5 * Trs(series_i)
    err_series = (Trs(mkt) - loc_series) / scale_series
    covar_series = []
    for i in range(err_series.shape[0]):
        covar_series.append(scipy.stats.norm(loc_series[i] + mu * scale_series[i], scale_series[i] * sigma).ppf(q))
    loc_series = pd.Series(loc_series, index = mkt.index, name = "loc")
    scale_series = pd.Series(scale_series, index = mkt.index, name = "scale")
    covar_series = pd.Series(covar_series, index = mkt.index, name = stock_name + "_CoVaR_" + str(q))
    error_series = pd.Series(err_series, index = mkt.index, name = "error_term")
    return covar_series, (mu, sigma), pd.concat([covar_series, error_series, loc_series, scale_series], axis = 1)


def MLE_covar(stock_name, q, qr_var_method, qr_var_modified = True,
              state_variables_series = stateVariables_W,
              market_losses_series = market_losses_W_pct):

    stk_var = var(stock_name, q, qr_var_method, qr_var_modified)
    var_i, mkt, svs_lagged = regularize(stk_var, market_losses_series, state_variables_series)
    params = fit_mle_norm(var_i, mkt, svs_lagged)
    return MLE_covar_result(params, stock_name, q, var_i, mkt, svs_lagged)


def MLE_delta_covar(stock_name, q, qr_var_method, qr_var_modified = True):
    if q <= 0.5 and q >= 1:
        raise Exception("Input Error! q should be in (0.5, 1)!")
    covar_MLE, stk_var = MLE_covar(stock_name, q, qr_var_method, qr_var_modified)[:2]
    temp = covar_MLE - MLE_covar(stock_name, 0.5, qr_var_method, qr_var_modified)[0]
    return temp.rename(stock_name + "_\u0394CoVaR_" + str(q)), stk_var


def var_params_MLE(stock_name, 
              market_losses_series = market_losses_W_pct, 
              stocks_losses_series = stocks_losses_W_pct, 
              state_variables_series = stateVariables_W):
    stk, mkt, svs_lagged = regularize(stocks_losses_series[stock_name], market_losses_series, state_variables_series)
    return fit_mle_norm(stk, mkt, svs_lagged), stk, mkt, svs_lagged


max_values = pd.DataFrame(columns = ["Max_Params", "Test_Params"])
params = pd.DataFrame(columns = list(stocks_losses_W_pct.columns))
for stock_name in list(stocks_losses_W_pct.columns):
    params[stock_name], stk, mkt, svs_lagged = var_params_MLE(stock_name)
    test_params = params[stock_name].copy()
    test_params[:] = [3, 1, 0, 0.3, -2, -0.2, 4, -2, -1, -9, 4, 8, -0.7, 1, 0.1, -2, 1, 2, 7, 3]
    max_values.loc[stock_name, "Max_Params"] = log_likelihood_norm(params[stock_name], stk, mkt, svs_lagged)
    max_values.loc[stock_name, "Test_Params"] = log_likelihood_norm(test_params, stk, mkt, svs_lagged)


params


max_values
False in (max_values["Max_Params"] > max_values["Test_Params"])

False


fig = plt.figure(figsize=(20, 12))
ax1 = fig.add_subplot(1, 1, 1)
threshold = -6000
max_vec = max_values[max_values["Test_Params"] >= threshold].loc[:, "Max_Params"]
test_vec = max_values[max_values["Test_Params"] >= threshold].loc[:, "Test_Params"]
for i in range(max_vec.shape[0]):
    y = np.linspace(test_vec.iloc[i], max_vec.iloc[i], 100)
    ax1.plot([max_vec.index[i]] * 100, y, color = "k", zorder = 1)
ax1.scatter(max_vec.index, max_vec, zorder = 2, label = "NLopt log-likelihood function values")
ax1.scatter(test_vec.index, test_vec, zorder = 2, label = "Test log-likelihood function values")
plt.xticks(fontsize=14, rotation = 90)
plt.yticks(fontsize=18)
plt.ylabel("Log-likelihood Function values", fontsize=18)
plt.legend(bbox_to_anchor=(0,-0.2), loc="lower left", fontsize=20)

[<matplotlib.lines.Line2D at 0x1511c317b88>]

[<matplotlib.lines.Line2D at 0x1511c317a48>]

[<matplotlib.lines.Line2D at 0x1511c317508>]

[<matplotlib.lines.Line2D at 0x1511c317f08>]

[<matplotlib.lines.Line2D at 0x1511c311cc8>]

[<matplotlib.lines.Line2D at 0x1511c321b48>]

[<matplotlib.lines.Line2D at 0x1511c321a48>]

[<matplotlib.lines.Line2D at 0x1511c328e88>]

[<matplotlib.lines.Line2D at 0x1511c328208>]

[<matplotlib.lines.Line2D at 0x1511c32cc08>]


def var_plot(stock_name, ax, q = 0.99, sector = sector, add_legend = False):
    historical = var(stock_name, q, historical_var)
    formula = var(stock_name, q, formula_var)
    qr_author = var(stock_name, q, qr_var, False)[int(window_size * 0.8):]
    qr_modified = var(stock_name, q, qr_var)[int(window_size * 0.8):]
    plot_min = np.array([historical.min(),formula.min(),qr_author.min(),qr_modified.min()]).min() - 5
    plot_max = np.array([historical.max(),formula.max(),qr_author.max(),qr_modified.max()]).max() + 35
    MLE = var(stock_name, q, MLE_var)[int(window_size * 0.8):]

    plt.title(sector[sector.index == stock_name]["Security"].values[0] + " - From " + sector[sector.index == stock_name]["GICS\xa0Sector"].values[0] + " Sector", fontsize=20)
    plt.ylabel("percent", fontsize=18)
    plt.ylim(plot_min, plot_max)
    plt.xticks(fontsize=16, rotation = 30)
    plt.yticks(fontsize=16)
    if add_legend:
        ax.plot(historical, label=str(int(100 *q)) + '%VaR - Nonparametric method')
        ax.plot(formula, label=str(int(100 *q)) + '%VaR - Semiparametric method')
        ax.plot(qr_author, label=str(int(100 *q)) + '%VaR - Parametric method [Quantile Regression - Author]')
        ax.plot(qr_modified, alpha = 0.8, label=str(int(100 *q)) + '%VaR - Parametric method [Quantile Regression - Modified (Add lagged stock losses series)]')
        ax.plot(MLE, label=str(int(100 *q)) + '%VaR - Parametric method [MLE]')
        plt.legend(bbox_to_anchor=(0,-0.4), loc="lower left", fontsize=20)
    else:
        ax.plot(historical)
        ax.plot(formula)
        ax.plot(qr_author)
        ax.plot(qr_modified, alpha = 0.8)
        ax.plot(MLE)


fig = plt.figure(figsize=(25, 22))
ax1 = fig.add_subplot(2, 3, 1)
var_plot("GS", ax1)
ax2 = fig.add_subplot(2, 3, 2)
var_plot("AAPL", ax2)
ax3 = fig.add_subplot(2, 3, 3)
var_plot("MMM", ax3)
ax4 = fig.add_subplot(2, 3, 4)
var_plot("ARE", ax4, add_legend = True)
ax5 = fig.add_subplot(2, 3, 5)
var_plot("CVS", ax5)
ax6 = fig.add_subplot(2, 3, 6)
var_plot("COP", ax6)


def covar_plot(stock_name, ax, q = 0.99, sector = sector, add_legend = False):
    MLE_MLE = MLE_covar(stock_name, q, MLE_var)[0]
    qr_MLE = MLE_covar(stock_name, q, qr_var)[0]
    qr_qr = qr_covar(stock_name, q, qr_var)[0]
    MLE_qr = qr_covar(stock_name, q, MLE_var)[0]
    
    if q == 0.5:
        plot_min = np.array([qr_qr, MLE_qr]).min() - 3
        plot_max = np.array([qr_qr, MLE_qr]).max() + 10
    else:
        plot_min = np.array([qr_qr, MLE_qr]).min()
        plot_max = np.array([qr_qr, MLE_qr]).max() + 70

    plt.title(sector[sector.index == stock_name]["Security"].values[0] + " - From " + sector[sector.index == stock_name]["GICS\xa0Sector"].values[0] + " Sector", fontsize=20)
    plt.ylabel("percent", fontsize=18)
    plt.ylim(plot_min, plot_max)
    plt.xticks(fontsize=16, rotation = 30)
    plt.yticks(fontsize=16)
    if add_legend:
        ax.plot(qr_MLE, label=str(int(100 *q)) + '%CoVaR - MLE - from ' + str(int(100 *q)) + '%VaR Quantile Regression')
        ax.plot(MLE_MLE, label=str(int(100 *q)) + '%CoVaR - MLE - from ' + str(int(100 *q)) + '%VaR MLE')
        ax.plot(qr_qr, label=str(int(100 *q)) + '%CoVaR - Quantile Regression - from ' + str(int(100 *q)) + '%VaR Quantile Regression')
        ax.plot(MLE_qr, label=str(int(100 *q)) + '%CoVaR - Quantile Regression - from ' + str(int(100 *q)) + '%VaR MLE')
        plt.legend(bbox_to_anchor=(0,-0.4), loc="lower left", fontsize=20)
    else:
        ax.plot(qr_MLE)
        ax.plot(MLE_MLE)
        ax.plot(qr_qr)
        ax.plot(MLE_qr)


fig = plt.figure(figsize=(25, 18))
ax1 = fig.add_subplot(2, 3, 1)
covar_plot("GS", ax1)
ax2 = fig.add_subplot(2, 3, 2)
covar_plot("AAPL", ax2)
ax3 = fig.add_subplot(2, 3, 3)
covar_plot("MMM", ax3)
ax4 = fig.add_subplot(2, 3, 4)
covar_plot("ARE", ax4, add_legend = True)
ax5 = fig.add_subplot(2, 3, 5)
covar_plot("CVS", ax5)
ax6 = fig.add_subplot(2, 3, 6)
covar_plot("COP", ax6)


fig = plt.figure(figsize=(25, 18))
ax1 = fig.add_subplot(2, 3, 1)
covar_plot("GS", ax1, q = 0.5)
ax2 = fig.add_subplot(2, 3, 2)
covar_plot("AAPL", ax2, q = 0.5)
ax3 = fig.add_subplot(2, 3, 3)
covar_plot("MMM", ax3, q = 0.5)
ax4 = fig.add_subplot(2, 3, 4)
covar_plot("ARE", ax4, q = 0.5, add_legend = True)
ax5 = fig.add_subplot(2, 3, 5)
covar_plot("CVS", ax5, q = 0.5)
ax6 = fig.add_subplot(2, 3, 6)
covar_plot("COP", ax6, q = 0.5)


def delta_covar_plot(stock_name, ax, q = 0.99, sector = sector, add_legend = False):
    MLE_MLE = MLE_delta_covar(stock_name, q, MLE_var)[0]
    qr_MLE = MLE_delta_covar(stock_name, q, qr_var)[0]
    qr_qr_1 = qr_delta_covar(stock_name, q, qr_var, formula_alter = False)[0]
    qr_qr_2 = qr_delta_covar(stock_name, q, qr_var)[0]

    if stock_name in ["GS", "ARE"]:
        plot_min = np.array([qr_qr_1]).min() - 15
        plot_max = np.array([qr_qr_1]).max() + 40
    elif stock_name == "AAPL":
        plot_min = np.array([qr_qr_2]).min() + 100
        plot_max = np.array([MLE_MLE]).max() - 50
    elif stock_name == "MMM":
        plot_min = np.array([qr_qr_2]).min()
        plot_max = np.array([qr_qr_1]).max() + 30
    elif stock_name == "COP":
        plot_min = np.array([qr_qr_2]).min()
        plot_max = np.array([qr_qr_1]).max() + 10
    else:
        plot_min = np.array([qr_qr_2]).min()
        plot_max = np.array([qr_qr_1]).max() + 60

    plt.title(sector[sector.index == stock_name]["Security"].values[0] + " - From " + sector[sector.index == stock_name]["GICS\xa0Sector"].values[0] + " Sector", fontsize=20)
    plt.ylabel("percent", fontsize=18)
    plt.ylim(plot_min, plot_max)
    plt.xticks(fontsize=16, rotation = 30)
    plt.yticks(fontsize=16)
    if add_legend:
        ax.plot(qr_qr_1, label=str(int(100 *q)) + '%\u0394CoVaR - Quantile Regression - Formula1 - from 99%VaR Quantile Regression')
        ax.plot(qr_qr_2, label=str(int(100 *q)) + '%\u0394CoVaR - Quantile Regression - Formula2 - from 99%VaR Quantile Regression')
        ax.plot(qr_MLE, label=str(int(100 *q)) + '%\u0394CoVaR - MLE - from 99%VaR Quantile Regression')
        ax.plot(MLE_MLE, label=str(int(100 *q)) + '%\u0394CoVaR - MLE - from 99%VaR MLE')
        plt.legend(bbox_to_anchor=(0,-0.4), loc="lower left", fontsize=20)
    else:
        ax.plot(qr_qr_1)
        ax.plot(qr_qr_2)
        ax.plot(qr_MLE)
        ax.plot(MLE_MLE)


fig = plt.figure(figsize=(25, 22))
ax1 = fig.add_subplot(2, 3, 1)
delta_covar_plot("GS", ax1)
ax2 = fig.add_subplot(2, 3, 2)
delta_covar_plot("AAPL", ax2)
ax3 = fig.add_subplot(2, 3, 3)
delta_covar_plot("MMM", ax3)
ax4 = fig.add_subplot(2, 3, 4)
delta_covar_plot("ARE", ax4, add_legend = True)
ax5 = fig.add_subplot(2, 3, 5)
delta_covar_plot("CVS", ax5)
ax6 = fig.add_subplot(2, 3, 6)
delta_covar_plot("COP", ax6)


def results_plot(stock_name, ax, q = 0.99, sector = sector, add_legend = False, market_losses_series = market_losses_W_pct):
    qr_modified = var(stock_name, q, qr_var)
    qr_qr = qr_delta_covar(stock_name, q, qr_var, formula_alter = False)[0]
    mkt = market_losses_series
    var_series = qr_modified
    delta_covar_series = qr_qr

    plt.title(sector[sector.index == stock_name]["Security"].values[0] + " - From " + sector[sector.index == stock_name]["GICS\xa0Sector"].values[0] + " Sector", fontsize=20)
    plt.ylabel("percent", fontsize=18)
    plt.xticks(fontsize=16, rotation = 30)
    plt.yticks(fontsize=16)
    if add_legend:
        ax.plot(mkt, label='Market Equity Loss')
        ax.plot(var_series, label=str(int(100 *q)) + '%\u0394CoVaR - Quantile Regression - Formula1 - from 99%VaR Quantile Regression')
        ax.plot(delta_covar_series, label=str(int(100 *q)) + '%VaR - Quantile Regression - Modified (Add lagged stock losses series)')
        plt.legend(bbox_to_anchor=(0,-0.4), loc="lower left", fontsize=20)
    else:
        ax.plot(mkt)
        ax.plot(var_series)
        ax.plot(delta_covar_series)


fig = plt.figure(figsize=(25, 17))
ax1 = fig.add_subplot(2, 3, 1)
results_plot("GS", ax1)
ax2 = fig.add_subplot(2, 3, 2)
results_plot("AAPL", ax2)
ax3 = fig.add_subplot(2, 3, 3)
results_plot("MMM", ax3)
ax4 = fig.add_subplot(2, 3, 4)
results_plot("ARE", ax4, add_legend = True)
ax5 = fig.add_subplot(2, 3, 5)
results_plot("CVS", ax5)
ax6 = fig.add_subplot(2, 3, 6)
results_plot("COP", ax6)


var_series_vec = pd.DataFrame(columns = list(stocks_losses_W_pct.columns))
delta_covar_series_vec = pd.DataFrame(columns = list(stocks_losses_W_pct.columns))
for stock_name in list(stocks_losses_W_pct.columns):
    delta_covar_series_vec[stock_name], var_series_vec[stock_name] = qr_delta_covar(stock_name, 0.99, qr_var, formula_alter = False)

C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)
C:\Users\Haochen Jiang\AppData\Roaming\Python\Python37\site-packages\statsmodels\regression\quantile_regression.py:192: IterationLimitWarning: Maximum number of iterations (1000) reached.
  ") reached.", IterationLimitWarning)


var_series_vec_corr = var_series_vec.copy()
delta_covar_series_vec_corr = delta_covar_series_vec.copy()
var_series_vec_corr["Market"] = market_losses_W_pct
delta_covar_series_vec_corr["Market"] = market_losses_W_pct


def print_model_summary(stock_name):
    print(qr_var(stock_name, 0.99)[1].summary())
    print(qr_covar(stock_name, 0.99, qr_var)[1].summary())


output_list = ["GS", "AAPL", "MMM", "ARE", "CVS", "COP"]
for stock_name in output_list:
    print_model_summary(stock_name)

                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:                     GS   Pseudo R-squared:               0.3845
Model:                       QuantReg   Bandwidth:                       2.374
Method:                 Least Squares   Sparsity:                        107.9
Date:                Fri, 20 May 2022   No. Observations:                  991
Time:                        17:42:21   Df Residuals:                      982
                                        Df Model:                            8
========================================================================================
                           coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------------
const                    5.0480      0.634      7.966      0.000       3.804       6.291
3MO_Yield_Change        -0.2192      0.068     -3.236      0.001      -0.352      -0.086
Term_Spread_Change       0.2333      0.328      0.711      0.477      -0.411       0.877
TED_Spread               0.0318      0.021      1.544      0.123      -0.009       0.072
Credit_Spread_Change     0.1241      0.649      0.191      0.848      -1.149       1.397
Market_Return           -0.1551      0.422     -0.368      0.713      -0.983       0.673
Excess_Return            0.0871      0.119      0.735      0.462      -0.145       0.320
Equity_Volatility        2.7503      1.175      2.341      0.019       0.445       5.056
stock_lagged            -0.1353      0.160     -0.845      0.399      -0.450       0.179
========================================================================================
                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:          Market_Losses   Pseudo R-squared:               0.3558
Model:                       QuantReg   Bandwidth:                       1.403
Method:                 Least Squares   Sparsity:                        50.78
Date:                Fri, 20 May 2022   No. Observations:                  991
Time:                        17:42:21   Df Residuals:                      982
                                        Df Model:                            8
========================================================================================
                           coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------------
const                    5.0712      2.136      2.374      0.018       0.879       9.263
3MO_Yield_Change        -0.1609      0.089     -1.812      0.070      -0.335       0.013
Term_Spread_Change       0.2053      0.144      1.429      0.153      -0.077       0.487
TED_Spread               0.0153      0.015      1.004      0.315      -0.015       0.045
Credit_Spread_Change     0.0248      0.156      0.159      0.874      -0.281       0.331
Market_Return           -0.4239      0.108     -3.911      0.000      -0.637      -0.211
Excess_Return           -0.1022      0.090     -1.138      0.256      -0.279       0.074
Equity_Volatility        4.2378      1.233      3.437      0.001       1.819       6.657
GS_VaR_0.99             -0.4983      0.422     -1.182      0.237      -1.326       0.329
========================================================================================
                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:                   AAPL   Pseudo R-squared:               0.1940
Model:                       QuantReg   Bandwidth:                       2.789
Method:                 Least Squares   Sparsity:                        169.2
Date:                Fri, 20 May 2022   No. Observations:                  991
Time:                        17:42:21   Df Residuals:                      982
                                        Df Model:                            8
========================================================================================
                           coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------------
const                    9.2568      1.817      5.094      0.000       5.691      12.823
3MO_Yield_Change        -0.1647      0.092     -1.795      0.073      -0.345       0.015
Term_Spread_Change      -0.1709      0.415     -0.412      0.680      -0.984       0.643
TED_Spread               0.0494      0.030      1.666      0.096      -0.009       0.108
Credit_Spread_Change     0.5221      0.588      0.889      0.374      -0.631       1.675
Market_Return           -0.3802      0.429     -0.887      0.375      -1.221       0.461
Excess_Return           -0.1185      0.107     -1.111      0.267      -0.328       0.091
Equity_Volatility       -0.9962      1.987     -0.501      0.616      -4.896       2.904
stock_lagged            -0.0147      0.219     -0.067      0.947      -0.445       0.416
========================================================================================
                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:          Market_Losses   Pseudo R-squared:               0.3627
Model:                       QuantReg   Bandwidth:                       1.385
Method:                 Least Squares   Sparsity:                        53.43
Date:                Fri, 20 May 2022   No. Observations:                  991
Time:                        17:42:21   Df Residuals:                      982
                                        Df Model:                            8
========================================================================================
                           coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------------
const                   59.9508     46.034      1.302      0.193     -30.386     150.287
3MO_Yield_Change        -1.0529      0.828     -1.272      0.204      -2.677       0.571
Term_Spread_Change      -0.9453      0.873     -1.083      0.279      -2.658       0.767
TED_Spread               0.2976      0.253      1.178      0.239      -0.198       0.794
Credit_Spread_Change     3.3478      2.648      1.264      0.207      -1.850       8.545
Market_Return           -2.6027      1.852     -1.406      0.160      -6.236       1.031
Excess_Return           -0.8442      0.612     -1.379      0.168      -2.045       0.357
Equity_Volatility       -3.6388      5.022     -0.725      0.469     -13.494       6.216
AAPL_VaR_0.99           -6.1277      4.986     -1.229      0.219     -15.912       3.657
========================================================================================

The condition number is large, 9.7e+03. This might indicate that there are
strong multicollinearity or other numerical problems.
                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:                    MMM   Pseudo R-squared:               0.1480
Model:                       QuantReg   Bandwidth:                       1.639
Method:                 Least Squares   Sparsity:                        119.9
Date:                Fri, 20 May 2022   No. Observations:                  991
Time:                        17:42:21   Df Residuals:                      982
                                        Df Model:                            8
========================================================================================
                           coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------------
const                    5.1777      0.673      7.691      0.000       3.857       6.499
3MO_Yield_Change         0.0280      0.182      0.154      0.878      -0.329       0.385
Term_Spread_Change      -0.0961      0.251     -0.383      0.702      -0.589       0.397
TED_Spread               0.0085      0.025      0.340      0.734      -0.041       0.058
Credit_Spread_Change    -0.0522      0.301     -0.173      0.862      -0.643       0.539
Market_Return           -0.3612      0.245     -1.476      0.140      -0.841       0.119
Excess_Return           -0.0138      0.138     -0.100      0.920      -0.284       0.257
Equity_Volatility        1.8123      0.713      2.540      0.011       0.412       3.212
stock_lagged            -0.0864      0.160     -0.539      0.590      -0.401       0.228
========================================================================================
                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:          Market_Losses   Pseudo R-squared:               0.3557
Model:                       QuantReg   Bandwidth:                       1.415
Method:                 Least Squares   Sparsity:                        56.70
Date:                Fri, 20 May 2022   No. Observations:                  991
Time:                        17:42:21   Df Residuals:                      982
                                        Df Model:                            8
========================================================================================
                           coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------------
const                    0.1764      6.881      0.026      0.980     -13.326      13.679
3MO_Yield_Change        -0.0671      0.051     -1.313      0.189      -0.167       0.033
Term_Spread_Change       0.1554      0.149      1.042      0.298      -0.137       0.448
TED_Spread              -0.0051      0.015     -0.345      0.730      -0.034       0.024
Credit_Spread_Change     0.0167      0.172      0.098      0.922      -0.320       0.354
Market_Return           -0.2576      0.437     -0.589      0.556      -1.116       0.600
Excess_Return           -0.1090      0.062     -1.770      0.077      -0.230       0.012
Equity_Volatility        2.0576      2.451      0.839      0.401      -2.753       6.868
MMM_VaR_0.99             0.4666      1.331      0.350      0.726      -2.146       3.079
========================================================================================

The condition number is large, 1.82e+03. This might indicate that there are
strong multicollinearity or other numerical problems.
                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:                    ARE   Pseudo R-squared:               0.4125
Model:                       QuantReg   Bandwidth:                       2.629
Method:                 Least Squares   Sparsity:                        102.6
Date:                Fri, 20 May 2022   No. Observations:                  991
Time:                        17:42:21   Df Residuals:                      982
                                        Df Model:                            8
========================================================================================
                           coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------------
const                    3.8848      0.883      4.399      0.000       2.152       5.618
3MO_Yield_Change         0.0108      0.050      0.215      0.830      -0.087       0.109
Term_Spread_Change       0.5247      0.203      2.587      0.010       0.127       0.923
TED_Spread              -0.0167      0.008     -2.105      0.036      -0.032      -0.001
Credit_Spread_Change    -0.2922      0.370     -0.789      0.430      -1.019       0.434
Market_Return           -0.7840      0.283     -2.768      0.006      -1.340      -0.228
Excess_Return           -0.1949      0.269     -0.724      0.469      -0.723       0.333
Equity_Volatility        6.3685      0.944      6.746      0.000       4.516       8.221
stock_lagged            -0.3145      0.235     -1.341      0.180      -0.775       0.146
========================================================================================
                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:          Market_Losses   Pseudo R-squared:               0.3689
Model:                       QuantReg   Bandwidth:                       1.401
Method:                 Least Squares   Sparsity:                        51.46
Date:                Fri, 20 May 2022   No. Observations:                  991
Time:                        17:42:21   Df Residuals:                      982
                                        Df Model:                            8
========================================================================================
                           coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------------
const                    4.1222      1.918      2.149      0.032       0.358       7.886
3MO_Yield_Change        -0.0458      0.030     -1.531      0.126      -0.105       0.013
Term_Spread_Change       0.2858      0.328      0.872      0.383      -0.357       0.929
TED_Spread              -0.0084      0.012     -0.677      0.498      -0.033       0.016
Credit_Spread_Change    -0.0687      0.165     -0.418      0.676      -0.392       0.254
Market_Return           -0.6066      0.207     -2.930      0.003      -1.013      -0.200
Excess_Return           -0.1383      0.083     -1.664      0.096      -0.301       0.025
Equity_Volatility        5.2605      2.942      1.788      0.074      -0.513      11.034
ARE_VaR_0.99            -0.3835      0.473     -0.810      0.418      -1.312       0.545
========================================================================================
                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:                    CVS   Pseudo R-squared:              0.08584
Model:                       QuantReg   Bandwidth:                       2.185
Method:                 Least Squares   Sparsity:                        116.1
Date:                Fri, 20 May 2022   No. Observations:                  991
Time:                        17:42:21   Df Residuals:                      982
                                        Df Model:                            8
========================================================================================
                           coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------------
const                    7.3797      0.781      9.454      0.000       5.848       8.912
3MO_Yield_Change         0.1346      0.161      0.835      0.404      -0.182       0.451
Term_Spread_Change      -0.6955      0.195     -3.564      0.000      -1.078      -0.313
TED_Spread               0.0457      0.012      3.671      0.000       0.021       0.070
Credit_Spread_Change    -0.1717      0.249     -0.689      0.491      -0.660       0.317
Market_Return           -0.2800      0.243     -1.152      0.250      -0.757       0.197
Excess_Return            0.3629      0.102      3.555      0.000       0.163       0.563
Equity_Volatility       -0.4699      0.674     -0.697      0.486      -1.792       0.852
stock_lagged            -0.1939      0.230     -0.843      0.400      -0.646       0.258
========================================================================================
                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:          Market_Losses   Pseudo R-squared:               0.3545
Model:                       QuantReg   Bandwidth:                       1.398
Method:                 Least Squares   Sparsity:                        61.17
Date:                Fri, 20 May 2022   No. Observations:                  991
Time:                        17:42:21   Df Residuals:                      982
                                        Df Model:                            8
========================================================================================
                           coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------------
const                    1.9818      2.385      0.831      0.406      -2.699       6.663
3MO_Yield_Change        -0.0786      0.055     -1.422      0.155      -0.187       0.030
Term_Spread_Change       0.1832      0.280      0.655      0.513      -0.366       0.732
TED_Spread              -0.0045      0.017     -0.267      0.790      -0.038       0.029
Credit_Spread_Change    -0.0244      0.189     -0.129      0.897      -0.396       0.347
Market_Return           -0.3747      0.147     -2.557      0.011      -0.662      -0.087
Excess_Return           -0.1514      0.135     -1.118      0.264      -0.417       0.114
Equity_Volatility        2.7957      0.326      8.583      0.000       2.156       3.435
CVS_VaR_0.99             0.1032      0.325      0.317      0.751      -0.536       0.742
========================================================================================
                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:                    COP   Pseudo R-squared:               0.2890
Model:                       QuantReg   Bandwidth:                       2.370
Method:                 Least Squares   Sparsity:                        125.6
Date:                Fri, 20 May 2022   No. Observations:                  991
Time:                        17:42:21   Df Residuals:                      982
                                        Df Model:                            8
========================================================================================
                           coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------------
const                    8.5687      0.690     12.414      0.000       7.214       9.923
3MO_Yield_Change        -0.2165      0.202     -1.070      0.285      -0.614       0.180
Term_Spread_Change      -0.1238      0.285     -0.434      0.664      -0.684       0.436
TED_Spread               0.0037      0.023      0.165      0.869      -0.041       0.048
Credit_Spread_Change     0.7432      0.262      2.841      0.005       0.230       1.257
Market_Return           -0.0830      0.302     -0.275      0.783      -0.675       0.509
Excess_Return           -0.0296      0.127     -0.234      0.815      -0.278       0.219
Equity_Volatility        1.2098      0.681      1.776      0.076      -0.127       2.547
stock_lagged            -0.1853      0.137     -1.348      0.178      -0.455       0.084
========================================================================================
                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:          Market_Losses   Pseudo R-squared:               0.3556
Model:                       QuantReg   Bandwidth:                       1.450
Method:                 Least Squares   Sparsity:                        60.93
Date:                Fri, 20 May 2022   No. Observations:                  991
Time:                        17:42:21   Df Residuals:                      982
                                        Df Model:                            8
========================================================================================
                           coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------------
const                    1.8341      3.788      0.484      0.628      -5.598       9.267
3MO_Yield_Change        -0.0329      0.103     -0.321      0.748      -0.234       0.168
Term_Spread_Change       0.0765      0.128      0.596      0.552      -0.176       0.329
TED_Spread              -0.0032      0.012     -0.275      0.783      -0.026       0.020
Credit_Spread_Change    -0.0311      0.389     -0.080      0.936      -0.795       0.733
Market_Return           -0.4099      0.140     -2.927      0.004      -0.685      -0.135
Excess_Return           -0.0770      0.064     -1.202      0.230      -0.203       0.049
Equity_Volatility        2.8947      0.568      5.093      0.000       1.779       4.010
COP_VaR_0.99             0.0893      0.442      0.202      0.840      -0.778       0.957
========================================================================================


sector_analyze1 = pd.DataFrame(index = ["\u0394CoVaR", "VaR", "Sector"], columns = list(delta_covar_series_vec.columns))
sector_analyze1.loc["VaR",:] = var_series_vec.iloc[-1,:]
sector_analyze1.loc["\u0394CoVaR",:] = delta_covar_series_vec.iloc[-1,:]
for stock_name in list(sector_analyze1.columns):
    sector_analyze1.loc["Sector", stock_name] = sector.loc[stock_name, "GICS\xa0Sector"]


sector_analyze2 = pd.DataFrame(index = ["\u0394CoVaR", "VaR", "Sector"], columns = list(delta_covar_series_vec.columns))
sector_analyze2.loc["VaR",:] = var_series_vec.iloc[-200,:]
sector_analyze2.loc["\u0394CoVaR",:] = delta_covar_series_vec.iloc[-200,:]
for stock_name in list(sector_analyze2.columns):
    sector_analyze2.loc["Sector", stock_name] = sector.loc[stock_name, "GICS\xa0Sector"]


sector_analyze3 = pd.DataFrame(index = ["\u0394CoVaR", "VaR", "Sector"], columns = list(delta_covar_series_vec.columns))
sector_analyze3.loc["VaR",:] = var_series_vec.iloc[-400,:]
sector_analyze3.loc["\u0394CoVaR",:] = delta_covar_series_vec.iloc[-400,:]
for stock_name in list(sector_analyze3.columns):
    sector_analyze3.loc["Sector", stock_name] = sector.loc[stock_name, "GICS\xa0Sector"]


sector_analyze4 = pd.DataFrame(index = ["\u0394CoVaR", "VaR", "Sector"], columns = list(delta_covar_series_vec.columns))
sector_analyze4.loc["VaR",:] = var_series_vec.iloc[-600,:]
sector_analyze4.loc["\u0394CoVaR",:] = delta_covar_series_vec.iloc[-600,:]
for stock_name in list(sector_analyze4.columns):
    sector_analyze4.loc["Sector", stock_name] = sector.loc[stock_name, "GICS\xa0Sector"]


sector_names = list(set(sector.loc[:, "GICS\xa0Sector"]))


def scatter(stock_name, ax, sector_analyze):
    ax.scatter(sector_analyze.loc["VaR", stock_name], sector_analyze.loc["\u0394CoVaR", stock_name])


fig = plt.figure(figsize=(25, 15))
ax1 = fig.add_subplot(2, 2, 1)
for i, stock_name in enumerate(list(delta_covar_series_vec.columns)):
    scatter(stock_name, ax1, sector_analyze1)
ax1.set_ylabel(str(var_series_vec.iloc[-1,:].name)[:10] + " \u0394CoVaR (percent)", fontsize=18)
ax1.set_xlabel(str(var_series_vec.iloc[-1,:].name)[:10] + " VaR (percent)", fontsize=18)
plt.xticks(fontsize=18)
plt.yticks(fontsize=18)

ax2 = fig.add_subplot(2, 2, 2)
for i, stock_name in enumerate(list(delta_covar_series_vec.columns)):
    scatter(stock_name, ax2, sector_analyze2)
ax2.set_ylabel(str(var_series_vec.iloc[-200,:].name)[:10] + " \u0394CoVaR (percent)", fontsize=18)
ax2.set_xlabel(str(var_series_vec.iloc[-200,:].name)[:10] + " VaR (percent)", fontsize=18)
plt.xticks(fontsize=18)
plt.yticks(fontsize=18)

ax3 = fig.add_subplot(2, 2, 3)
for i, stock_name in enumerate(list(delta_covar_series_vec.columns)):
    scatter(stock_name, ax3, sector_analyze3)
ax3.set_ylabel(str(var_series_vec.iloc[-400,:].name)[:10] + " \u0394CoVaR (percent)", fontsize=18)
ax3.set_xlabel(str(var_series_vec.iloc[-400,:].name)[:10] + " VaR (percent)", fontsize=18)
plt.xticks(fontsize=18)
plt.yticks(fontsize=18)

ax4 = fig.add_subplot(2, 2, 4)
for i, stock_name in enumerate(list(delta_covar_series_vec.columns)):
    scatter(stock_name, ax4, sector_analyze4)
ax4.set_ylabel(str(var_series_vec.iloc[-600,:].name)[:10] + " \u0394CoVaR (percent)", fontsize=18)
ax4.set_xlabel(str(var_series_vec.iloc[-600,:].name)[:10] + " VaR (percent)", fontsize=18)
plt.xticks(fontsize=18)
plt.yticks(fontsize=18)

Text(0, 0.5, '2022-01-02 ΔCoVaR (percent)')

Text(0.5, 0, '2022-01-02 VaR (percent)')

(array([ 0.,  5., 10., 15., 20., 25., 30., 35.]),
 [Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, '')])

(array([ 2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.]),
 [Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, '')])

Text(0, 0.5, '2018-03-11 ΔCoVaR (percent)')

Text(0.5, 0, '2018-03-11 VaR (percent)')

(array([ 0.,  5., 10., 15., 20., 25., 30., 35.]),
 [Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, '')])

(array([ 6.,  7.,  8.,  9., 10., 11., 12.]),
 [Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, '')])

Text(0, 0.5, '2014-05-11 ΔCoVaR (percent)')

Text(0.5, 0, '2014-05-11 VaR (percent)')


diver_names = ["BAC", "C", "CMA", "JPM", "USB", "WFC"]
inves_names = ["SCHW", "GS", "MS"]
insur_names = ["AFL", "GL", "MET", "PFG", "PRU"]
consu_names = ["AXP", "COF", "DFS"]
names_list = [diver_names, inves_names, insur_names, consu_names]
color_list = ["b", "r", "k", "g"]
marker_list = ["o", "^", "v", "+"]
x_adjust_list_1 = list(np.array([-0.09,0.02,0.02,-0.15]) / 3.5)
y_adjust_list_1 = list(np.array([0.05,0.02,-0.1,-0.1]) / 3.5)
x_adjust_list_2 = list(np.array([-0.09,0.02,0.02,-0.15]) / 3)
y_adjust_list_2 = list(np.array([0.05,0.02,-0.1,-0.1]) / 3)
x_adjust_list_3 = list(np.array([-0.09,0.02,0.02,-0.15]) / 3)
y_adjust_list_3 = list(np.array([0.05,0.02,-0.1,-0.1]) / 3)
x_adjust_list_4 = list(np.array([-0.09,0.02,0.02,-0.15]) / 1.75)
y_adjust_list_4 = list(np.array([0.05,0.02,-0.1,-0.1]) / 1.75)
label_list = ["Diversified Banks", "Investment Banking & Brokerage", "Life & Health Insurance", "Consumer Finance"]


fig = plt.figure(figsize=(25, 20))
ax1 = fig.add_subplot(2, 2, 1)
for i, stock_name_list in enumerate(names_list):
    for stock_name in stock_name_list:
        ax1.scatter(sector_analyze1.loc["VaR", stock_name], 
                    sector_analyze1.loc["\u0394CoVaR", stock_name], 
                    color = color_list[i], s = 100, 
                    marker = marker_list[i])
        plt.text(sector_analyze1.loc["VaR", stock_name] + x_adjust_list_1[i], 
                 sector_analyze1.loc["\u0394CoVaR", stock_name] + y_adjust_list_1[i],
                 stock_name, fontsize=14)
    ax1.set_ylabel(str(var_series_vec.iloc[-1,:].name)[:10] + " \u0394CoVaR (percent)", fontsize=18)
    ax1.set_xlabel(str(var_series_vec.iloc[-1,:].name)[:10] + " VaR (percent)", fontsize=18)
    plt.xticks(fontsize=18)
    plt.yticks(fontsize=18)

ax2 = fig.add_subplot(2, 2, 2)
for i, stock_name_list in enumerate(names_list):
    for stock_name in stock_name_list:
        ax2.scatter(sector_analyze2.loc["VaR", stock_name], 
                    sector_analyze2.loc["\u0394CoVaR", stock_name], 
                    color = color_list[i], s = 100, 
                    marker = marker_list[i])
        plt.text(sector_analyze2.loc["VaR", stock_name] + x_adjust_list_2[i], 
                 sector_analyze2.loc["\u0394CoVaR", stock_name] + y_adjust_list_2[i],
                 stock_name, fontsize=14)
    ax2.set_ylabel(str(var_series_vec.iloc[-200,:].name)[:10] + " \u0394CoVaR (percent)", fontsize=18)
    ax2.set_xlabel(str(var_series_vec.iloc[-200,:].name)[:10] + " VaR (percent)", fontsize=18)
    plt.xticks(fontsize=18)
    plt.yticks(fontsize=18)

ax3 = fig.add_subplot(2, 2, 3)
for i, stock_name_list in enumerate(names_list):
    for stock_name in stock_name_list:
        ax3.scatter(sector_analyze3.loc["VaR", stock_name], 
                    sector_analyze3.loc["\u0394CoVaR", stock_name], 
                    color = color_list[i], s = 100, 
                    marker = marker_list[i])
        plt.text(sector_analyze3.loc["VaR", stock_name] + x_adjust_list_3[i], 
                 sector_analyze3.loc["\u0394CoVaR", stock_name] + y_adjust_list_3[i],
                 stock_name, fontsize=14)
    ax3.set_ylabel(str(var_series_vec.iloc[-400,:].name)[:10] + " \u0394CoVaR (percent)", fontsize=18)
    ax3.set_xlabel(str(var_series_vec.iloc[-400,:].name)[:10] + " VaR (percent)", fontsize=18)
    plt.xticks(fontsize=18)
    plt.yticks(fontsize=18)
    
ax3.scatter(sector_analyze3.loc["VaR", "BAC"],  sector_analyze3.loc["\u0394CoVaR", "BAC"], 
            color = color_list[0], s = 100, marker = marker_list[0], label = label_list[0])
ax3.scatter(sector_analyze3.loc["VaR", "SCHW"],  sector_analyze3.loc["\u0394CoVaR", "SCHW"], 
            color = color_list[1], s = 100, marker = marker_list[1], label = label_list[1])
ax3.scatter(sector_analyze3.loc["VaR", "AFL"],  sector_analyze3.loc["\u0394CoVaR", "AFL"], 
            color = color_list[2], s = 100, marker = marker_list[2], label = label_list[2])
ax3.scatter(sector_analyze3.loc["VaR", "AXP"],  sector_analyze3.loc["\u0394CoVaR", "AXP"], 
            color = color_list[3], s = 100, marker = marker_list[3], label = label_list[3])
plt.legend(bbox_to_anchor=(0,-0.4), loc="lower left", fontsize=20)

ax4 = fig.add_subplot(2, 2, 4)
for i, stock_name_list in enumerate(names_list):
    for stock_name in stock_name_list:
        ax4.scatter(sector_analyze4.loc["VaR", stock_name], 
                    sector_analyze4.loc["\u0394CoVaR", stock_name], 
                    color = color_list[i], s = 100, 
                    marker = marker_list[i])
        plt.text(sector_analyze4.loc["VaR", stock_name] + x_adjust_list_4[i], 
                 sector_analyze4.loc["\u0394CoVaR", stock_name] + y_adjust_list_4[i],
                 stock_name, fontsize=14)
    ax4.set_ylabel(str(var_series_vec.iloc[-600,:].name)[:10] + " \u0394CoVaR (percent)", fontsize=18)
    ax4.set_xlabel(str(var_series_vec.iloc[-600,:].name)[:10] + " VaR (percent)", fontsize=18)
    plt.xticks(fontsize=18)
    plt.yticks(fontsize=18)

<matplotlib.collections.PathCollection at 0x1512335e208>

Text(11.025310660712211, 4.82812136839541, 'BAC')

<matplotlib.collections.PathCollection at 0x151229dd2c8>

Text(13.421559521066646, 4.979035634702523, 'C')

<matplotlib.collections.PathCollection at 0x151229d3b48>

Text(8.940643752705556, 5.257030080622478, 'CMA')

<matplotlib.collections.PathCollection at 0x1510e930748>

Text(7.711832384028402, 4.796355613705203, 'JPM')

<matplotlib.collections.PathCollection at 0x1510e930c08>

Text(9.737030807870857, 5.113862877769345, 'USB')


def sector_plot(ax, j, sector_analyze, legend = False, sector_names = sector_names, v = var_series_vec):
    color_list = ['blue', 'orange', 'green', 'red', 'purple', 'brown', 'pink', 'gray', 'olive', 'cyan', "black"]
    for i, sector_name in enumerate(sector_names):
        temp = sector_analyze.loc[:, sector_analyze.loc["Sector",:] == sector_name]
        ax.scatter(temp.loc["VaR"], temp.loc["\u0394CoVaR"], color = color_list[i], label = sector_name)
        ax.set_ylabel(str(v.iloc[-j,:].name)[:10] + " \u0394CoVaR (percent)", fontsize=18)
        ax.set_xlabel(str(v.iloc[-j,:].name)[:10] + " VaR (percent)", fontsize=18)
        plt.xticks(fontsize=18)
        plt.yticks(fontsize=18)
        if legend:
            plt.legend(bbox_to_anchor=(0,-0.9), loc="lower left", fontsize=20)


fig = plt.figure(figsize=(25, 18))
ax1 = fig.add_subplot(2, 2, 1)
sector_plot(ax1, 1, sector_analyze1)
ax2 = fig.add_subplot(2, 2, 2)
sector_plot(ax2, 200, sector_analyze2)
ax3 = fig.add_subplot(2, 2, 3)
sector_plot(ax3, 400, sector_analyze3, legend = True)
ax4 = fig.add_subplot(2, 2, 4)
sector_plot(ax4, 600, sector_analyze4)

	MMM	AOS	ABT	ABBV	ABMD	ACN	ATVI	ADM	ADBE	ADP	...	WMB	WTW	WYNN	XEL	XYL	YUM	ZBRA	ZBH	ZION	ZTS
0	-0.593409	-0.312086	-0.413222	-0.141634	-0.448963	-0.302434	-0.151775	0.062371	0.220366	-0.250235	...	-0.238580	-0.316262	-0.206955	-0.638256	0.206177	-0.059334	-0.342791	-0.360442	0.209166	-0.752245
1	0.304903	0.348305	0.346725	0.248250	0.311587	0.308979	0.303314	0.303780	0.337508	0.264152	...	0.347177	0.325032	0.254997	0.212796	0.295467	0.305347	0.333449	0.328461	0.315391	0.260009
2	2.900682	-0.028710	2.378961	-2.720184	1.453672	-0.850722	-0.229370	-2.552167	-3.111008	-0.940264	...	-0.107328	-1.175360	0.048824	-0.180683	-0.900945	0.060527	-0.243206	-0.335869	-2.753388	7.124727
3	0.189153	0.188525	0.258063	0.024341	0.156796	0.118914	0.123243	0.000598	0.136935	0.041975	...	-0.162098	0.234018	0.164274	-0.043330	-0.100433	0.193989	0.042768	0.100873	0.062900	0.005246
4	0.953512	-0.047069	0.028129	0.487649	0.191251	0.407374	0.100183	0.006225	0.195955	0.130066	...	-0.140465	-0.232250	-0.081703	0.252342	0.028188	-0.270096	0.262176	0.098542	0.152388	0.235737
5	0.201684	0.194480	0.203328	0.180928	0.189693	0.208437	0.197625	0.166165	0.180771	0.198141	...	0.176940	0.193396	0.181672	0.192718	0.260920	0.177184	0.203493	0.203121	0.199417	0.271690
6	0.043302	0.323177	0.588991	-0.043655	-1.422947	0.192092	0.513455	-0.318575	-0.184435	0.327794	...	1.155302	0.735836	0.134231	0.003060	-0.177554	0.277297	-0.095870	0.502489	0.230006	0.216485
7	0.711959	0.234291	0.963591	0.031950	0.399652	1.083671	0.404721	0.089443	-0.444359	-0.005357	...	0.252600	0.504174	0.124458	0.004588	-0.470181	0.338761	0.101600	0.325555	0.310023	0.329484
8	0.384342	0.093310	0.556777	-0.055902	0.267303	0.356691	-0.112418	-0.077550	-0.061032	-0.177075	...	-0.117127	0.210439	0.255684	0.686932	-0.189749	0.129206	0.380159	0.276297	0.142917	0.162213
9	1.569032	0.518762	0.270970	0.456367	0.729194	0.682479	-0.167666	-3.527279	-3.409657	0.094243	...	-0.580183	0.825879	0.570677	-0.227252	-4.543779	0.202253	-0.998459	0.071429	-1.718285	0.688400
10	2.753715	0.107971	0.534162	0.163717	-0.704851	0.396334	3.225652	-0.449285	0.668838	-0.098824	...	-0.079963	0.558092	-0.762773	-2.164645	2.011886	1.308700	0.616175	1.616364	1.313551	0.174156
11	5.213459	6.019918	6.114866	4.367412	5.442481	5.328669	8.140916	7.838512	5.136429	6.327876	...	8.372590	6.114176	5.431660	5.779553	8.180928	6.386957	4.382704	5.620795	5.244928	6.004869
12	0.095628	0.172525	0.284202	0.783390	0.210527	0.704736	0.123888	0.323476	-0.005170	0.138028	...	0.086540	0.251348	0.140119	0.266448	0.246862	0.216869	0.203853	0.096972	0.214852	0.206168
13	0.911315	1.366515	0.309813	0.335979	-0.990807	0.310607	0.206292	-1.589365	-0.584215	0.759049	...	-0.047486	-0.124508	1.327687	0.250566	-1.521734	-0.063421	0.284564	0.610200	0.220993	0.336490
14	0.203431	0.194250	0.224512	0.282407	0.199117	0.212738	0.210626	0.118650	0.283838	0.241159	...	0.278805	0.229689	0.209822	0.286500	0.221421	0.201937	0.230225	0.236223	0.299092	0.278186
15	0.954357	0.594206	0.328071	0.435051	0.128434	1.703367	1.133346	-1.111123	-1.208614	0.185070	...	-0.047628	1.544605	-0.189319	0.069276	0.296894	0.088691	0.535190	0.304615	-0.320812	0.200915
16	0.071798	0.194811	-0.904123	1.017898	0.213527	0.425862	0.260742	-1.341487	0.357740	0.730372	...	0.180972	0.483443	0.290696	0.092373	0.108629	0.255912	0.355929	-0.053439	-0.325867	0.135143
17	0.171477	0.286548	1.373528	-0.093262	0.176910	0.240904	0.333000	0.449816	0.288833	-0.312052	...	0.107920	0.285392	-0.004091	1.053342	-0.647412	0.377137	0.126733	-0.047722	0.064389	0.212846
18	6.298553	5.584104	9.159393	5.382258	4.870595	2.700370	6.294277	5.010385	5.457088	5.720679	...	5.487325	5.271616	5.461442	5.353551	5.828038	5.663894	5.177705	7.252333	5.605523	5.320002
19	0.380678	2.786513	3.393228	2.626716	-2.764579	2.729649	0.251198	4.099338	-0.996234	2.966177	...	-0.249661	3.194625	3.408782	-1.698298	-3.130028	0.007019	2.916957	2.587023	-1.723819	-0.006971

	Max_Params	Test_Params
MMM	59.824164	-17957.347338
AOS	40.293151	-5589.749471
ABT	46.145184	-13205.302339
ABBV	154.673997	-43363.961696
ABMD	151.899154	-10013782.830008
...	...	...
YUM	23.248764	-648333.43476
ZBRA	48.744118	-7341.665783
ZBH	106.409432	-5367.079748
ZION	69.886101	-80872932.686062
ZTS	138.644758	-924932.803433

VaR Calculation¶

Nonparametric method - Historical Data¶

Semiparametric method - Formula¶

Parametric method - MLE¶

Parametric method - Quantile Regression¶

Summary Function¶

$\Delta$CoVaR Calculation¶

Quantile Regression¶

MLE (Maximum Likelihood Estimation)¶

Empirical Study¶

MLE Algorithm Robustness Testing¶

VaR computational methods comparison¶

CoVar computational methods comparison¶

$\Delta$CoVaR computational methods comparison¶

$\Delta$CoVaR and VaR Results¶

Sectors Analysis¶

Appendix¶

1 FRED-DTB3 - 3months Fred Treasury bill rate in secondary market¶

2 USTREASURY-LONGTERMRATES - Composite Long term bond yield¶

3 USTREASURY-LONGTERMRATES - 3 months libor rate¶

4 FRED-DGS3MO - 3 months tbill constant maturity rate¶

5 Change in Credit Spread¶